The new alliance developing in this country between Jews and fundamentalist evangelicals, two groups that have traditionally regarded each other with suspicion or worse, will take a tentative step forward next month in events scheduled for two Washington synagogues.

The common ground for the new linkage is Israel.

On Nov. 12, several hundred conservative evangelicals will join members of Washington Hebrew Congregation in a Solidarity for Israel Sabbath. Rabbi Joshua O. Haberman, who called the event an attempt to "build bridges," will share the pulpit of the city's largest Reform synagogue with the Rev. Paige Patterson, president of the Criswell Center for Biblical Studies in Dallas. Patterson is a leader of the fundamentalist faction that has been seeking to wrest control of the Southern Baptist Convention from moderates.

The night before, supporters of the California-based evangelical group called TAV, augmented by what a TAV leader described as a "40-piece band, with dancing," will gather at Beth Shalom, together with, they hope, members of that Orthodox synagogue. Dr. John Walvoord, president of the Dallas Theological Seminary, and a representative of the government of Israel are slated to address the gathering.

Moshe Teichman, Beth Shalom's executive director, emphasized that the event was under the sponsorship of the Zionist Organization of America, not the synagogue. "They are just using our facilities," he said.

Also scheduled is a dialogue between Jewish and evangelical leaders in a panel that is expected to include Ed McAteer, head of the politically right-wing Religious Roundtable; Ben Armstrong, executive of the National Religious Broadcasters, and "Pat Robertson or Jerry Falwell or both or neither," according to TAV leader Doug Krieger.

TAV, a name taken from the last letter of the Hebrew alphabet, has also initiated at least one private conference with Conservative and Orthodox Jewish leaders in New York. Next month, First Baptist Church in Dallas has scheduled a pro-Israel rally at which Israeli Prime Minister Menachem Begin is slated to receive an award.

For nearly half a century in this country, the Jewish-Christian dialogue has been almost entirely with Catholics and liberal Protestants. Jews were repelled by the zeal of evangelicals to convert them to Christianity; some of the more fundamentalist evangelical groups were the focus of more overt forms of anti-Semitism.

Only a little more than two years ago, the then president of the Southern Baptist Convention outraged Jews as well as many of his coreligionists with the statement that "God doesn't hear the prayer of a Jew."

Eighteen months ago, at the 75th anniversary meeting of the American Jewish Committee here, seminars and workshops on the threat to Jews from such right-wing evangelical movements as the Moral Majority drew standing-room-only crowds.

What has brought about the new rapprochement is Israel. Fundamentalist Christians view Israel not in political but in biblical terms, as the fulfillment of divine prophecy. The support of fundamentalist evangelicals "is rooted in an uncompromising adherence to scriptural passages which promise that land to the Jews," said Douglas R. Shearer of TAV.

Liberal Protestants and Catholics, on the other hand, view Israel more in the political context, and while defending it as a homeland for the Jews, they do not hesitate to question political and military actions.

Traditional Jewish-Christian good relations took a hard pounding from the events in the Middle East in recent months, as mainline Protestant leaders issued statements increasingly critical of Israel's actions in Lebanon. Even more damaging was Pope John Paul's decision to meet with Palestine Liberation Organization leader Yasser Arafat.

The growing pressure on Israel, explained Rabbi Marc Tanenbaum of the American Jewish Committee, "has led to extraordinary anxiety and a sense of desperation among Jews . . . .

"Under these circumstances, when you have evangelical Christians, who may number 40 or 50 million Americans, reaching out in love and support, Jews tend to be quite pragmatic; they look at the bottom line of reality." As for the traditional fears about conversion pressures from fundamentalists, he said, "It's like if you are drowning and someone throws you a life preserver. You grab it and worry later about who manufactured the life preserver. The first worry is survival."

Tanenbaum's interreligious affairs committee has conducted two Jewish-Baptist theological dialogues, in which the Southern Baptist participants tended to come from the more progressive wing of evangelicalism. The issue of efforts to convert Jews remained unresolved in those discussions.

Krieger, whose TAV group has conducted five West Coast interfaith services like the one projected at Washington Hebrew, agreed that "most evangelicals are going to be very anxious to see Jews brought to the Messiah, because they have the obligation in scripture to do this."

At the same time, he said, "we feel Christians must be active and see their responsibility for the Jewish community. The support that the evangelical Christian has for the Jew throughout the world does not cease to be vibrant if the Jew does not embrace Christianity."

Haberman, recently elected president of the Washington Board of Rabbis, has a record of crashing religious barriers. In early 1978, he invited Wallace D. Muhammad, head of the American Muslim Mission, formerly the Black Muslims, to participate in what turned out to be a highly amicable pulpit exchange. He has also been active in less controversial interfaith activities.

"I have always believed that the attitude of a religious community to another is the acid test of its own credentials," Haberman said in discussing the upcoming solidarity Sabbath. "If a hand is stretched out in my direction, I am going to grasp that hand."